More by Clarence W. Wilkerson

Abstract

Let $R$ be a graded subalgebra of a polynomial ring $S$
over a field so that $S$ is algebraic over $R$. The goal of
this paper is to relate the generator degrees of $R$ to the
degree $[S:R]$ of the underlying quotient field extension, and
to provide a numerical criterion for $S$ to be integral over
$R$ that is based on this relationship. As an application we
obtain a condition guaranteeing that a ring of invariants of a
finite group is a polynomial ring.